ΔABC ~ ΔPQR, the areas of ΔABC and ΔPQR are 64 cm2 and 81 cm2, respectively and AD and PT are the medians of ΔABC and ΔPQR, respectively. If PT = 10.8 cm, then AD = ?

This question was previously asked in
SSC CGL 2020 Tier-I Official Paper 1 (Held On : 13 Aug 2021 Shift 1)
View all SSC CGL Papers >
  1. 9 cm
  2. 12 cm
  3. 8.4 cm
  4. 9.6 cm

Answer (Detailed Solution Below)

Option 4 : 9.6 cm
super-pass-live
Free
SSC CGL Tier 1 2025 Full Test - 01
3.5 Lakh Users
100 Questions 200 Marks 60 Mins

Detailed Solution

Download Solution PDF

Given:

ΔABC ~ ΔPQR

Area of ΔABC = 64 cm2

Area of ΔPQR = 81 cm2

PT = 10.8 cm 

AD is the median of ΔABC.

PT is the median of ΔPQR

Concept: 

F1 Ashish Madhu 19.10.21 D2

The ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides & medians. 

\(\text{Area of (ΔABC)}\over{\text{Area of (ΔPQR)}}\) = \(({AD\over PT})^2\)

Calculation:

\(\text{Area of (ΔABC)}\over{\text{Area of (ΔPQR)}}\) = \(({AD\over PT})^2\)

⇒ \(64\over81\) = \(({AD\over PT})^2\) 

​ \(AD\over PT\) = \(\sqrt{64\over81}\) = \(8\over9\)

​ \(AD\over 10.8\) = \(8\over9\)

​ AD = \({8\times10.8}\over9\) = 9.6 cm

∴ AD = 9.6 cm 

Latest SSC CGL Updates

Last updated on Jul 16, 2025

-> This year, the Staff Selection Commission (SSC) has announced approximately 14,582 vacancies for various Group B and C posts across government departments.

-> The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025.

->  Aspirants should visit ssc.gov.in 2025 regularly for updates and ensure timely submission of the CGL exam form.

-> Candidates can refer to the CGL syllabus for a better understanding of the exam structure and pattern.

-> The CGL Eligibility is a bachelor’s degree in any discipline.

-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.

-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.

-> The Bihar Sakshamta Pariksha Admit Card 2025 for 3rd phase is out on its official website.

More Triangles, Congruence and Similarity Questions

Get Free Access Now
Hot Links: teen patti gold teen patti rummy teen patti master king